# Discrete math: logical equivalent statement and statement forms "Two statement forms are called log

Discrete math: logical equivalent statement and statement forms
"Two statement forms are called logically equivalent if, and only if, they have identical truth values for each possible substitution of statements for their statement variables... denoted $P\equiv Q$.
Two statements are called logically equivalent if, and only if , they have logically equivalent forms when identical component statement variables are used to replace identical component statements."
Later in the exercise section she writes: $p="x>5"$. Do you not use $\equiv$ for statement definitions and if so, how do you symbolise equivalence between two statements, $p\equiv q$ or $p=q$.
Since p and q by them selves could technically be seen as statement forms, is there a difference between $p\equiv q$ and $p=q$?
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Franco Cohen
Step 1
$p=q$ means the two statements are identical, i.e. that they are one single statement.
$p\equiv q$ means that the two statements are equivalent, but not (necessarily) identical.
Step 2
For example, if p is the statement $x>5$, while q is the statement " $\mathrm{¬}\left(x\le 5\right)$", then the two statements are equivalent, but they are not identical.